(7x-2)(2-3x)+(4x+3x)(7x-2)=0

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Solution for (7x-2)(2-3x)+(4x+3x)(7x-2)=0 equation: 


Simplifying
(7x + -2)(2 + -3x) + (4x + 3x)(7x + -2) = 0

Reorder the terms:
(-2 + 7x)(2 + -3x) + (4x + 3x)(7x + -2) = 0

Multiply (-2 + 7x) * (2 + -3x)
(-2(2 + -3x) + 7x * (2 + -3x)) + (4x + 3x)(7x + -2) = 0
((2 * -2 + -3x * -2) + 7x * (2 + -3x)) + (4x + 3x)(7x + -2) = 0
((-4 + 6x) + 7x * (2 + -3x)) + (4x + 3x)(7x + -2) = 0
(-4 + 6x + (2 * 7x + -3x * 7x)) + (4x + 3x)(7x + -2) = 0
(-4 + 6x + (14x + -21x2)) + (4x + 3x)(7x + -2) = 0

Combine like terms: 6x + 14x = 20x
(-4 + 20x + -21x2) + (4x + 3x)(7x + -2) = 0

Combine like terms: 4x + 3x = 7x
-4 + 20x + -21x2 + (7x)(7x + -2) = 0

Remove parenthesis around (7x)
-4 + 20x + -21x2 + 7x(7x + -2) = 0

Reorder the terms:
-4 + 20x + -21x2 + 7x(-2 + 7x) = 0
-4 + 20x + -21x2 + (-2 * 7x + 7x * 7x) = 0
-4 + 20x + -21x2 + (-14x + 49x2) = 0

Reorder the terms:
-4 + 20x + -14x + -21x2 + 49x2 = 0

Combine like terms: 20x + -14x = 6x
-4 + 6x + -21x2 + 49x2 = 0

Combine like terms: -21x2 + 49x2 = 28x2
-4 + 6x + 28x2 = 0

Solving
-4 + 6x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3x + 14x2) = 0

Factor a trinomial.
2((-1 + -2x)(2 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-0.5, 0.2857142857}

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